Towards a Localized Version of Pearson`s Correlation Coefficient

Abstract

Pearson`s correlation coeffcient is used to describe dependence between random variables X and Y. In some practical situations,however,we have strong correlation for some values X and/or Y and no correlation for other values of X and Y. To describe such a local dependence,we come up with a natural localized version of Pearson`s correlation coefficient. We also study the properties of the newly defined localized coefficient.